Delocalization transition at larger Trotter step size

Determine whether, in the translationally invariant Trotterized dynamics of the Z2 lattice gauge theory implemented here (with gauge-mediated Ising interactions of strength J, gauge polarization h, matter polarization μ, and Floquet step size Δt), there exists a phase transition to a delocalized phase when the Trotter step Δt is increased beyond the regime where approximate energy conservation yields localized energy transport.

Background

The paper investigates disorder-free localization using a translationally invariant Floquet unitary U_LGT that Trotterizes a Z2 lattice gauge theory with matter and gauge qubits, observing localized energy transport in both one and two dimensions.

The experiments and simulations focus on a regime of small Trotter step Δt where the total energy is approximately conserved under the Floquet dynamics, leading to behavior consistent with many-body localization in the observed timescales. Increasing Δt reduces the quality of this approximate conservation and could potentially induce delocalization, but whether this change leads to a bona fide phase transition remains unresolved.